If the open strings buzz on the first fret, raise that side of the nut with a shim. Otherwise, it isn't a nut problem. Fret at the first fret and see where the buzzing happens. A little more
neck relief might help, or you might have a couple high or loose fret ends. I'd expect buzzing in the 5-7 fret area if you didn't have enough relief, but not necessarily. Raising the action on that side might help too, depending on where it is now.